Discrete Random Variable and Probability Mass Function

In this class, We discuss Discrete Random variables and Probability Mass Function.

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The reader should have prior knowledge of random variables and probability distribution. Click Here.

Random variables are of two types.

1) Discrete random variable

2) Continuous random variable

Discrete Random Variable:

A random variable that contains a finite number of discrete values in an interval is called a discrete random variable.

Example:

Toss three coins

Random variable X = Number of heads

Sample space = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

The below table shows the probability distribution of random variable X.

The interval of random variable X is 0-3.

The random variable X takes a finite set of discrete values in the interval. So X is a discrete random variable.

In the interval, if the random variable considers all the values, we say it is a continuous random variable.

Two conditions should be satisfied by the probability mass function.

1) f(x) >= 0 for each real number x.

The function f(x) providing probability values. so always greater or equal to zero.

2) Σall x f(x) = 1

The sum of all the probability values should equal one.

A function satisfying the two conditions is considered for the probability mass function.